DOUBLE PRECISION FUNCTION DBESY0(X)
C***BEGIN PROLOGUE  DBESY0
C***DATE WRITTEN   770701   (YYMMDD)
C***REVISION DATE  820801   (YYMMDD)
C***CATEGORY NO.  C10A1
C***KEYWORDS  BESSEL FUNCTION,DOUBLE PRECISION,ORDER ZERO,SECOND KIND,
C             SPECIAL FUNCTION
C***AUTHOR  FULLERTON, W., (LANL)
C***PURPOSE  Computes the d.p. Bessel function of the second kind of
C            order zero.
C***DESCRIPTION
C
C DBESY0(X) calculates the double precision Bessel function of the
C second kind of order zero for double precision argument X.
C
C Series for BY0        on the interval  0.          to  1.60000E+01
C                                        with weighted error   8.14E-32
C                                         log weighted error  31.09
C                               significant figures required  30.31
C                                    decimal places required  31.73
C***REFERENCES  (NONE)
C***ROUTINES CALLED  D1MACH,D9B0MP,DBESJ0,DCSEVL,INITDS,XERROR
C***END PROLOGUE  DBESY0
      DOUBLE PRECISION X, BY0CS(19), AMPL, THETA, TWODPI, XSML,
     1  Y, Z, D1MACH, DCSEVL, DBESJ0
      DATA BY0 CS(  1) / -.1127783939 2865573217 9398054602 8 D-1      /
      DATA BY0 CS(  2) / -.1283452375 6042034604 8088453183 8 D+0      /
      DATA BY0 CS(  3) / -.1043788479 9794249365 8176227661 8 D+0      /
      DATA BY0 CS(  4) / +.2366274918 3969695409 2415926461 3 D-1      /
      DATA BY0 CS(  5) / -.2090391647 7004862391 9622395034 2 D-2      /
      DATA BY0 CS(  6) / +.1039754539 3905725209 9924657638 1 D-3      /
      DATA BY0 CS(  7) / -.3369747162 4239720967 1877534503 7 D-5      /
      DATA BY0 CS(  8) / +.7729384267 6706671585 2136721637 1 D-7      /
      DATA BY0 CS(  9) / -.1324976772 6642595914 4347606896 4 D-8      /
      DATA BY0 CS( 10) / +.1764823261 5404527921 0038936315 8 D-10     /
      DATA BY0 CS( 11) / -.1881055071 5801962006 0282301206 9 D-12     /
      DATA BY0 CS( 12) / +.1641865485 3661495027 9223718574 9 D-14     /
      DATA BY0 CS( 13) / -.1195659438 6046060857 4599100672 0 D-16     /
      DATA BY0 CS( 14) / +.7377296297 4401858424 9411242666 6 D-19     /
      DATA BY0 CS( 15) / -.3906843476 7104373307 4090666666 6 D-21     /
      DATA BY0 CS( 16) / +.1795503664 4361579498 2912000000 0 D-23     /
      DATA BY0 CS( 17) / -.7229627125 4480104789 3333333333 3 D-26     /
      DATA BY0 CS( 18) / +.2571727931 6351685973 3333333333 3 D-28     /
      DATA BY0 CS( 19) / -.8141268814 1636949333 3333333333 3 D-31     /
      DATA TWODPI / 0.6366197723 6758134307 5535053490 057 D0 /
      DATA NTY0, XSML / 0, 0.D0 /
C***FIRST EXECUTABLE STATEMENT  DBESY0
      IF (NTY0.NE.0) GO TO 10
      NTY0 = INITDS (BY0CS, 19, 0.1*SNGL(D1MACH(3)))
      XSML = DSQRT (4.0D0*D1MACH(3))
C
 10   IF (X.LE.0.D0) CALL XERROR ( 'DBESY0  X IS ZERO OR NEGATIVE', 29,
     1  1, 2)
      IF (X.GT.4.0D0) GO TO 20
C
      Y = 0.D0
      IF (X.GT.XSML) Y = X*X
      DBESY0 = TWODPI*DLOG(0.5D0*X)*DBESJ0(X) + .375D0 + DCSEVL (
     1  .125D0*Y-1.D0, BY0CS, NTY0)
      RETURN
C
 20   CALL D9B0MP (X, AMPL, THETA)
      DBESY0 = AMPL * DSIN(THETA)
      RETURN
C
      END